Explicit upper bounds for |L(1,χ)| when χ(3) = 0
Let χ be a primitive Dirichlet character of conductor q and denote by L(z,χ) the associated L-series. We provide an explicit upper bound for |L(1,χ)| when 3 divides q.
Exponential sums and additive problems involving square-free numbers
Exponentialsummen und Nullstellen von L-Reihen.
Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series.
Extension of Estermann’s theorem to Euler products associated to a multivariate polynomial
Given a multivariate polynomial with integral coefficients verifying an hypothesis of analytic regularity (and satisfying ), we determine the maximal domain of meromorphy of the Euler product and the natural boundary is precisely described when it exists. In this way we extend a well known result for one variable polynomials due to Estermann from 1928. As an application, we calculate the natural boundary of the multivariate Euler products associated to a family of toric varieties.
Extensions of asymptotic expansions from Chapter 15 of Ramanujan's second notebook.
Extrait d'un travail intitulé «Sur le mémoire de Riemann relatif au nombre des nombres premiers inférieurs à une grandeur donnée»
Extremal values of Dirichlet -functions in the half-plane of absolute convergence
We prove that for any real there are infinitely many values of with and such thatThe proof relies on an effective version of Kronecker’s approximation theorem.
Extreme values of argL(1,χ)
Extreme values of the Dedekind zeta function
Extreme values of the Riemann zeta function.
Extreme values of the Riemann zeta-function on short zero intervals
Factorization of constants involved in conjectural moments of zeta-functions.
Familles de fonctions de formes automorphes et applications
Une notion importante qui a émergé de la théorie analytique des fonctions ces dernières années, est celle de famille. Par exemple les familles de fonctions interviennent naturellement dans le modèle probabiliste des matrices aléatoires de Katz/Sarnak qui vise à prédire la répartition des zéros des fonctions . L’analyse des fonctions en famille intervient également dans la résolution (inconditionnelle) de divers problèmes ayant une signification arithmétique profonde, tel que le problème de...
Farey series and the Riemann hypothesis
Faster and faster convergent series for .
Finite cotangent sums and the Riemann zeta function
Flows of Mellin transforms with periodic integrator
We study Mellin transforms for which is periodic with period in order to investigate ‘flows’ of such functions to Riemann’s and the possibility of proving the Riemann Hypothesis with such an approach. We show that, excepting the trivial case where , the supremum of the real parts of the zeros of any such function is at least .We investigate a particular flow of such functions which converges locally uniformly to as , and show that they exhibit features similar to . For example, ...
Fonction L des courbes modulaires
Fonction -adique associée à un caractère de Dirichlet